Method of measuring the error rate of an optical transmission system and apparatus for implementing the method

ABSTRACT

The present invention relates to a method of measuring the error rate of an optical transmission system transmitting a signal, said method comprising the following operations:  
     detecting the signal,  
     asynchronously sampling the signal at a frequency independent of the bit rate of the signal to obtain K samples of the signal at respective times t 1  to t K  where K is an integer greater than or equal to 2,  
     computing the eye diagram of the signal, and  
     computing the error rate of the signal.  
     After sampling the signal, the method further comprises an operation of computing the bit time of the signal.

[0001] The present invention relates to a method of measuring the errorrate of an optical transmission system and apparatus for implementingthe method.

[0002] Optical networks are increasingly used nowadays in high bit ratetransmission systems. Optical networks provide functions, such asswitching, that are transparent, i.e. independent of the electricalsignal transmitted, and thus offer the flexibility required in moderntelecommunication networks.

[0003] However, this transparency necessitates verifying that the signaltransmitted conforms to what is required, in particular in terms oftransmission quality. It is therefore essential to have transparentmeans for determining the quality of the signal transmittedindependently of the format of the signal, in particular itstransmission bit rate and its type of modulation, in order to be able tomeasure the quality of optical transmission over any type of network(backbone network, MAN, LAN, etc.) regardless of its data format (SONET,SDH, IP over WDM, Giga-Ethernet, etc.) and its bit rate (622 Mbit/s, 2.5Gbit/s, 10 Gbit/s, etc.).

[0004] There are many causes of signal degradation in optical networks.They include amplified spontaneous emission (ASE) by amplifiers,chromatic dispersion generating inter-symbol interference (ISI),out-band crosstalk (linked to an adjacent channel) and in-band crosstalk(caused by an interfering wave at the same wavelength as that measured).These causes of degradation are additional to non-linear effects such asthe Kerr, Brillouin, and Raman effects.

[0005] The principal quality criterion of a digital optical network isits bit error rate (BER), which is defined as the probability of thereceiver detecting an erroneous bit. Because of noise, the signalreceived at the receiver fluctuates around an average value I₁ (if a 1was transmitted) or I₀ (if a 0 was transmitted). It is assumed that thedistribution is Gaussian in both cases. The distribution of the 1 leveltherefore has as its parameters I₁ and the variance σ² ₁, while thedistribution of the 0 level has as its parameters I₀ and the variance σ²₀. To decide if a value received by the receiver is correct, it isnecessary to impose a decision threshold I_(D). A bit sent at 1 isconsidered to be correct if I>I_(D) and a bit sent at 0 is considered tobe correct if I<I_(D) In other words, an error has occurred if I<I_(D)for a bit sent at 1 or if I>I_(D) for a bit sent at 0. In practice,I_(D) is optimized to minimize the BER.

[0006] The BER is defined by the equation:${BER} = \frac{\exp \left( {{- Q^{2}}/2} \right)}{Q \cdot \sqrt{2 \cdot \pi}}$

[0007] in which Q, referred to as the quality factor, is defined by theequation: $Q = \frac{I_{1} - I_{0}}{\sigma_{0} - \sigma_{1}}$

[0008] A method of determining the quality of an optical signalindependently of the format of the signal by using relative error ratemeasurements is already available.

[0009] This method, described in the document “Field Trial over 750 kmlong transparent WDM link using an adaptive 10 Gb/s receiver withnon-intrusive monitoring capability”, S. Herbst et al., OFC 2001 (paperML2-1), for example, is based on measuring the amplitude of the detectedelectrical signal by using an exclusive-OR function to compare thedecisions of two bistables, one operating at the optimum threshold I_(D)(optimum amplitude from which the signal is considered to be equal to 1)and the other operating with a variable amplitude threshold. Thedifference between the signals from the two bistables, referred as thepseudo-error, is logged each time that the two measurements aredifferent. Assuming a Gaussian distribution of the levels, extrapolatingthe pseudo-error rate curves as a function of the position of thevariable amplitude threshold provides an evaluation of the BER at theoptimum threshold.

[0010] The above method is intrinsically transparent to the format ofthe signal transmitted. However, it necessitates the use of a clockrecovery circuit and a variable delay line for phase adjustment. Thesecomponents introduce a non-negligible cost factor and additionally limitthe transparency of the method because they cannot be tuned over a widerange of signal bit rates.

[0011] Another method of solving this problem, known as the histogrammethod, is also available. This method applies asynchronous sampling tothe transmitted signal, so that the sampling is independent of the bitrate of the signal, after which all of the samples are placed on theamplitude axis. A histogram representing the number of samples as afunction of amplitude is then extracted. Then, after eliminatingproblematical points using a heuristic method, an estimate is derivedfrom the histogram using two Gaussian distributions to determine the Qfactor and then the BER.

[0012] That method is not always satisfactory. It provides only aqualitative evaluation of the error rate, because the results that itsupplies are not reliable.

[0013] An object of the present invention is therefore to provide amethod of measuring the error rate of an optical transmission systemthat is transparent not only to the format of the transmitted signal butalso to the signal transmission bit rate, and which necessitates the useof components that are less costly than the prior art method.

[0014] To this end, the present invention proposes a method of measuringthe error rate of an optical transmission system transmitting a signal,said method comprising the following operations:

[0015] detecting said signal,

[0016] asynchronously sampling said signal at a frequency independent ofthe bit rate of said signal to obtain K samples of said signal atrespective times t₁ to t_(K) where K is an integer greater than or equalto 2,

[0017] computing the eye diagram of said signal, and

[0018] computing the error rate of said signal,

[0019] which method is characterized in that, after sampling saidsignal, it further comprises an operation of computing the bit time ofsaid signal.

[0020] The method of the invention solves the problem caused by theprior art methods using asynchronous sampling, namely the inaccuracy ofthe result. The method of the invention computes the bit time so thatthe same advantages are obtained as with a synchronous method using aphysical clock recovery system, but the clock recovery system is nolonger necessary. The method of the invention is also transparent to thetransmission bit rate.

[0021] By means of the invention, the eye diagram can be reconstructedwithout knowing the bit rate, i.e. without knowing the real bit time ofthe optical signal, because it is computed from the signal sampledasynchronously.

[0022] Furthermore, asynchronous sampling of the received optical signalguarantees that the method of the invention is transparent to the typeof modulation. The asynchronous sampling can be carried out at afrequency very much lower than the bit rates used, which means that itis not synchronized to the signal.

[0023] Computing the bit time of the signal is an essential step forreconstituting the eye diagram when the sampling is asynchronous.

[0024] Note that, in the context of the invention, the expression “bittime” is used both for the absolute bit time and for the bit timerelative to the sampling frequency.

[0025] In a first implementation of the method of the invention, theabsolute bit time is computed from an approximate value To knowninitially.

[0026] To this end, simultaneous computation of the bit time and the eyediagram comprises the following operations:

[0027] choosing a sub-sample of K/N samples of said signal where N is aninteger power of 2,

[0028] separating said sub-sample into two parts,

[0029] computing two eye diagrams from the respective parts of thesub-sample using the value T₀ for the bit time,

[0030] computing two histograms from the two eye diagrams by digitizingthe time and the intensity,

[0031] determining the time period δ between the two histograms,

[0032] determining the bit time T₁ from the equation:${T_{1} = {T_{0} - {2\quad \delta \frac{T_{0}}{t_{k}}}}},{and}$

[0033] repeating the above operations substituting N/2 for N until asub-sample of K/2 samples is obtained.

[0034] This implementation is particularly simple and necessitates onlya very approximate initial knowledge of the bit time; furthermore, itcomputes very accurately the real bit time, which differs greatly fromthe bit time known initially because of the inaccuracy relating to thesignal clock. This implementation also reconstitutes the eye diagram.

[0035] In a second implementation of the method of the invention, thebit time relative to the sampling frequency is computed withoutinitially knowing the bit time.

[0036] To this end, the following operations are effected:

[0037] applying a non-linear function to the series of samples of thesignal to obtain a series of substantially periodic values y_(k) for kvarying from 1 to K,

[0038] dividing the series into M sub-series each of L elements where Land M are integers,

[0039] computing the discrete Fourier transform of each sub-series,which yields a function Y_(i) for i varying from 1 to M,

[0040] defining a periodogram function as the ratio with respect to M ofthe sum of the squares of the moduli of the functions Y_(i) for ivarying from 1 to M, and

[0041] determining the frequency f which maximizes the periodogramfunction.

[0042] To compute the eye diagram, the following operations are theneffected:

[0043] computing the discrete Fourier transform at the frequency f ofthe series y_(k), which yields a function z_(k) for k varying from 1 toK, and

[0044] obtaining the time associated with each sample of the signal fromthe equation:$\tau_{k} = \frac{\arg \left( Z_{k} \right)}{2\quad \pi}$

[0045] In an advantageous implementation, the Fourier transform iscomputed over a sliding window centered on y_(k). This avoids errors dueto cumulative phase jitter affecting the sampling clock or the signal.

[0046] This second implementation dispenses completely with the need forany initial knowledge of the bit time, and it improves tolerance tojitter affecting the sampling clock or the signal.

[0047] In the invention, when the bit time has been determined and theeye diagram reconstituted by either of the above methods, the error rateis computed by modeling the statistical distributions of the levels ofthe signal by means of P Gaussian distributions where P is an integergreater than or equal to 2 and preferably equal to 8. This takes betteraccount of the deterministic levels resulting from inter-symbolinterference.

[0048] Finally, the invention also provides apparatus for implementingthe above method, which apparatus comprises:

[0049] means for detecting the signal,

[0050] means for sampling the detected signal at a frequency independentof the bit rate of the signal,

[0051] means for digitizing samples obtained at the output of thesampling means, and

[0052] software for processing the digitized samples to compute the bittime and the eye diagram.

[0053] The software can also model the statistical distributions of thelevels in order to compute the error rate of the signal.

[0054] Other features and advantages of the present invention becomeapparent in the course of the following description of an embodiment ofthe invention, which is provided by way of illustrative and non-limitingexample.

[0055] In the accompanying drawings:

[0056]FIG. 1 shows the architecture of apparatus for measuring the errorrate of an optical transmission system using a method of the invention,and

[0057]FIG. 2 shows a typical “eye diagram” of an optical signal.

[0058]FIG. 1 shows the architecture of apparatus 1 for measuring theerror rate of an optical transmission system using a method of theinvention, two implementations of which are described below withreference to this figure.

[0059] The optical signal S is received by a receiver 10. The receiver10 includes a PIN photodiode 11 which converts light into voltage. Amicrowave module 12 then eliminates the DC component of the electricalsignal from the photodiode 11. The electrical signal from the module 12is then amplified by two amplifiers 13 and then filtered by a filter 14.The filtering applied by the filter 14 must be matched to the bit rateto guarantee a good signal-to-noise ratio at the input of the sampler20.

[0060] The amplified and filtered electrical signal S′ is then sampledasynchronously in the sampler 20. The sampler includes a sampler head 21which samples the input signal at a given clock frequency, for example50 kHz. At the output of the sampler head 21 there is therefore obtainedan analog signal which can be treated as a series of impulse responses.Each impulse response has an amplitude that depends directly on theamplitude of the input signal in the sampler head 21.

[0061] As can be seen in FIG. 1, the sampler head 21 is connected tomeans 22 internal to the sampler 20 which provide it, via a cable (notshown), with the necessary power supply and a trigger signal T1commanding sampling of the input signal. The signal T1 is generated byan internal timebase 220 of the means 22.

[0062] The impulse analog signal SE from the sampler head 21 is thendigitized in a personal computer (PC) 30 by a digitizer card 31. Theinternal timebase 220 also supplies a trigger signal T2 to the digitizercard 31.

[0063] The digitized data is then stored in the PC 30 and then processedin accordance with the invention by software 32. The processing iseffected in three parts: a first part consists in recovering the bittime, a second part consists in reconstituting the eye diagram, and thethird part consists in determining the error rate, and thus the qualityfactor, from the reconstituted eye diagram.

[0064] The above three steps are described in detail below for each ofthe two implementations of a method of the invention.

[0065] 1^(st) Implementation

[0066] 1^(st) Part: Recovering the Bit Time and Computing the EyeDiagram

[0067] This step in fact amounts to effecting clock recovery insoftware, which avoids using a costly clock recovery circuit that is nottransparent to the transmission bit rate.

[0068] In this first implementation of the invention, the absolute bittime is computed from an approximate value To known initially.

[0069] To this end, a sub-sample {tilde over (E)} from the set ofsamples x_(k), with k varying from 1 to K, of the sampled signal SE istaken from the sampler head 21. This sub-sample includes K/N elements,where N is an integer power of 2 (typically 32 or 64).

[0070] The sub-sample {tilde over (E)} is divided into two parts {tildeover (E)}₁ and {tilde over (E)}₂.

[0071] The eye diagram of each of these two parts, representing theamplitude as a function of time of each sample from the respective parts{tilde over (E)}₁ and {tilde over (E)}₂, is computed using the value T₀for the bit time.

[0072] From these two eye diagrams, two histograms H₁ and H₂ areconstructed by digitizing the time and the current. The histograms areidentical except for a time period δ.

[0073] Let N₁ and N₂ denote the common sizes of the two histograms onthe time and current axes, respectively. The following equation appliesfor i varying from 0 to N₁:${C(i)} = \left. {\sum\limits_{j = 1}^{N_{1}}\quad \sum\limits_{k = 1}^{N_{2}}}\quad \middle| {{H_{1}\left( {{\left( {i + j} \right){{mod}N}_{1}},k} \right)} - {H_{2}\left( {j,k} \right)}} \middle| {}_{2}. \right.$

[0074] The value of i₀ is then determined, where C(i₀) is the greatestof the values C(i), and if i₀ is greater than N₁/2, then:

i ₀ =i ₀ −N ₁,

and: δ=i ₀ *T ₀ /t _(k).

[0075] The bit time T₁ is then determined using the equation:$T_{1} = {T_{0} - {2\quad \delta {\frac{T_{0}}{t_{k}}.}}}$

[0076] The above operations are iterated with N/2 substituted for Nuntil a sub-sample of K/2 samples is obtained.

[0077] A very accurate estimate of the bit time is then obtained, whichcircumvents the uncertainty regarding the value T₀ known initially.

[0078] Note that to estimate very small disturbances of the bit time, itis possible to apply the above operations once only, for N=1.

[0079] By means of this method, bit time recovery and eye diagramreconstitution are effected simultaneously. It then remains only todetermine the error rate.

[0080] Knowing the information relating to the bit time, the phase ofeach of the samples can be determined and the eye diagram can thereforebe reconstituted.

[0081] The eye diagram corresponds to a representation of all possibletransitions of an optical signal (to be more precise of the electricalsignal obtained at the output of the PIN diode), over a period of thesignal, i.e. over one bit time. FIG. 2 shows the diagram obtained, whichgives the amplitude of the optical signal as a function of time moduloT₀. It is called an “eye diagram” because the curve obtained iseye-shaped.

[0082] 2^(nd) Part: Determining the Error Rate BER

[0083] The eye diagram corresponding to optical transmission in thepresence of signal degradation, for example amplified spontaneousemission (ASE), but with no inter-symbol interference (ISI), takesaccount of the widening of the traces on the “1” and “0” levels. Thus anamplitude distribution is associated with each level: amplitudehistograms for each of the statistical distributions of the two levels.FIG. 2 shows the associated amplitude frequency histograms alongside theeye diagram of the above kind of signal.

[0084] The probability density function for each of the twodeterministic levels 1 and 0 is Gaussian. Thus each of the two levels isassociated with a standard deviation and with an average value. Theerror rate BER is determined from these parameters, and is directlyrelated to the quality factory Q by a known equation, as mentionedabove.

[0085] In the presence of inter-symbol interference, and because oftemporal widening caused by chromatic dispersion, for example, theoptical pulses can be superposed in amplitude. In this case, todetermine the error rate and the Q factor in accordance with theinvention, it is preferable to replace the model using two Gaussiandistributions described above with a model using eight Gaussiandistributions. Account is taken of interference between the bit beforeand the bit after a given bit, which yields eight deterministic levels(four for the 1 level and four for the 0 level), each of which can beassociated with a Gaussian distribution.

[0086] The parameters (average and variance) of these eight Gaussiandistributions can be estimated using the expectation-maximization (EM)algorithm described, for example, in “Maximum Likelihood for IncompleteData via the EM Algorithm (with discussion)”, Dempster, A. P. Laird, N.M. and Rubin, D. B. (1977), Journal of the Royal Statistics Society, B,39, 1-38, and is not described in more detail here.

[0087] In practice, the eye diagram is divided into N intervals. Foreach of these intervals, an approximation of the Q factor is computedbased on values of the intensities of the samples of the eye diagram.Let Y denote the set of all values of the intensities of a giveninterval, M₁ a median value of the set Y, Y₀ ⁺ the subset of valuesgreater than M₁, and Y₀ ⁻ the subset of values less than M₁.

[0088] The average m₀ ⁺ of the values Y₀ ⁺ and the average m₀ ⁻ of thevalues Y₀ ⁻ are then computed.

[0089] Y₀ ⁺ is then defined as the subset of Y such that:

|y−m ₀ ⁺ |≦|y−m ₀ ⁻|,

[0090] and Y⁻ is defined as the subset of Y such that:

|y−m ₀ ⁺ |>|y−m ₀ ⁻|,

[0091] Finally, m⁺ and σ⁺, the average and standard deviation of Y⁺, andm⁻ and σ⁻, the average and the standard deviation of Y⁻, are thencomputed.

[0092] The estimated Q factor for the given interval is then given bythe equation: $Q = \frac{m^{+} - m^{-}}{\sigma^{+} + \sigma^{-}}$

[0093] This yields a set of values Q(j) for j varying from 0 to N, andthe value of j₀ giving the greatest value of Q(j) is determined. Thisdetermines the central slice of the eye diagram.

[0094] The error rate is then evaluated by modeling with eight Gaussiandistributions over each of the slices on respective opposite sides ofthe central slice, the averages and variances being again estimatedusing the EM algorithm mentioned above. The minimum error ratedetermined in this way corresponds to the optimum Q factor.

[0095] The quality factor or Q factor is directly related to the errorrate BER by the equation given above. In practice, the method usingeight Gaussian distributions computes the error rate directly, and theequivalent Q factor is deduced from the error rate using the equationgiven above.

[0096] 2^(nd) Implementation

[0097] 1^(st) Part: Recovering the Bit Time and Computing the EyeDiagram

[0098] In this second implementation of the invention, the bit timerelating to the sampling frequency is computed without initially knowingthe bit time. The bit time relating to the sampling frequency issufficient to reconstitute the eye diagram.

[0099] To this end, a non-linear function is first applied to the seriesof samples x_(k) of the signal, to obtain a series of substantiallyperiodic values (i.e. values in which the periodic element isstrengthened) y_(k) for k varying from 1 to K. For example:${y_{k} = \left| {x_{k} - \overset{\_}{x}} \right|^{p}},{{{where}\quad \overset{\_}{x}} = {\frac{1}{K}{\sum\limits_{k = 0}^{K - 1}\quad {x_{k}.}}}}$

[0100] The series obtained in this way is then divided into M sub-serieseach of L elements (where L and M are integers).

[0101] The discrete Fourier transform of each sub-series is thencomputed, which yields a function Y_(i) for i varying from 1 to M:${Y_{i}\left( ^{j\quad \omega} \right)} = {\sum\limits_{k = 0}^{L - 1}\quad {y_{{1L} + k} \cdot {^{{- j}\quad k\quad \omega}.}}}$

[0102] The periodogram function P(e^(jω)) is then defined as being theratio with respect to M of the sum of the squares of the moduli of thefunctions Y_(i) for i varying from 1 to M.

[0103] The frequency f which maximizes the periodogram function isdetermined.

[0104] By using a sliding window, this algorithm in accordance with theinvention for recovering the bit time relating to the sampling frequencyavoids errors caused by the cumulative phase jitter of the samplingclock or the signal. The phase jitter of the clock is the uncertaintywith respect to the sampling times, which leads to a cumulative timeerror on each sample. The phase jitter of the signal is inherent to thesignal itself.

[0105] Then, to compute the eye diagram, the discrete Fourier transformat the frequency f is computed for the series y_(k), which yields afunction z_(k) for k varying from 1 to K. To this end, the Fourier sumis effected over 2F+1 points centered on the sample y_(k). Thus asliding window is used centered on y_(k) as a function of the sample.

[0106] The time associated with each sample x_(k) of the signal is thengiven by the equation:$\tau_{k} = \frac{\arg \left( Z_{k} \right)}{2\quad \pi}$

[0107] It is then easy to plot the eye diagram: the sample x_(k) is atthe position (τ_(k), x_(k)).

[0108] In accordance with the invention, by using a sliding window, theabove algorithm for recovering the bit time relating to the samplingfrequency and reconstituting the eye diagram avoids errors due to thecumulative phase jitter of the sampling clock or the signal. The phasejitter of the clock is the uncertainty with respect to the samplingtimes, which leads to a cumulative time error on each sample. The phasejitter of the signal is inherent to the signal itself.

[0109] 2^(nd) Part: Determining the Error Rate BER

[0110] Exactly the same method can be used as described with referenceto the first implementation.

[0111] Of course, the invention is not limited to the implementationsdescribed above. Thus double sampling can be employed with a time offsetof the order of one bit time between the two sampled signals, instead ofsingle sampling.

[0112] Finally, any means described can be replaced by equivalent meanswithout departing from the scope of the invention.

1. A method of measuring the error rate of an optical transmissionsystem transmitting a signal, said method comprising the followingoperations: detecting said signal, asynchronously sampling said signalat a frequency independent of the bit rate of said signal to obtain Ksamples of said signal at respective times t₁ to t_(K) where K is aninteger greater than or equal to 2, computing the eye diagram of saidsignal, and computing the error rate of said signal, which method ischaracterized in that, after sampling said signal, it further comprisesan operation of computing the bit time of said signal.
 2. A methodaccording to claim 1, characterized in that the absolute bit time iscomputed from an approximate value T₀ known initially.
 3. A methodaccording to claim 2, characterized in that simultaneous computation ofthe bit time and the eye diagram comprises the following operations:choosing a sub-sample of K/N samples of said signal where N is aninteger power of 2, separating said sub-sample into two parts, computingtwo eye diagrams from the respective parts of the sub-sample using thevalue T₀ for the bit time, computing two histograms from the two eyediagrams by digitizing the time and the intensity, determining the timeperiod δ between the two histograms, determining the bit time T₁ fromthe equation:${T_{1} = {T_{0} - {2\delta \frac{T_{0}}{t_{k}}}}},\quad {and}$

repeating the above operations substituting N/2 for n until a sub-sampleof K/2 samples is obtained.
 4. A method according to claim 1,characterized in that computing the bit time relating to the samplingfrequency comprises the following operations: applying a non-linearfunction to the series of samples of the signal to obtain a series ofsubstantially periodic values y_(k) for k varying from 1 to K, dividingthe series into M sub-series each of L elements where L and M areintegers, computing the discrete Fourier transform of each sub-series,which yields a function Y_(i) for i varying from 1 to M, defining aperiodogram function as the ratio with respect to M of the sum of thesquares of the moduli of the functions Y_(i) for i varying from 1 to M,and determining the frequency f which maximizes the periodogramfunction.
 5. A method according to claim 4, characterized in that, tocompute the eye diagram, the following operations are effected:computing the discrete Fourier transform at the frequency f of theseries y_(k), which yields a function z_(k) for k varying from 1 to K,and obtaining the time associated with each sample of the signal fromthe equation: $\tau_{k} = \frac{\arg \left( Z_{k} \right)}{2\pi}$


6. A method according to claim 5, characterized in that the Fouriertransform is computed over a sliding window centered on y_(k).
 7. Amethod according to any one of claims 1 to 6, characterized in that theerror rate is computed by modeling the statistical distributions of thelevels of said signal by means of P Gaussian distributions where P is aninteger greater than or equal to 2 and preferably equal to
 8. 8. Amethod according to claim 7, characterized in that when P is equal to 8the average and the variance of the eight Gaussian distributions areestimated by applying the expectation-maximization (EM) algorithm. 9.Apparatus for measuring the error rate of an optical transmission systemtransmitting a signal, which device is characterized in that itincludes: means (10) for detecting a signal (S) that has beentransmitted by the optical transmission system, means (20) for samplingsaid detected signal (S′) at a frequency independent of the bit rate ofsaid signal, means (31) for digitizing samples (SE) obtained at theoutput of said sampling means (20), and software (32) for processingsaid digitized samples to compute said bit time, said eye diagram andthe error rate of said signal.
 10. Apparatus according to claim 9,characterized in that said software (32) also models the statisticaldistributions of the levels of the signal in order to compute the errorrate of the signal.